Matrix Completion with Non-uniform Missing Patterns, a New Measure of Conditional Dependence, and Applications to Feature Selection

具有非均匀缺失模式的矩阵补全、条件依赖性的新度量以及在特征选择中的应用

基本信息

  • 批准号:
    2113242
  • 负责人:
  • 金额:
    $ 30万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Standard Grant
  • 财政年份:
    2021
  • 资助国家:
    美国
  • 起止时间:
    2021-07-15 至 2024-06-30
  • 项目状态:
    已结题

项目摘要

This project aims to study three classes of problems in mathematical statistics. The first class of problems is about matrix completion. Suppose that we have an array of numbers with missing entries, such as a database of ratings from users of a product. Matrix completion is the problem of predicting the missing values. Much work has been done on this problem in the last ten years, but the vast majority of it is under the assumption that the matrix entries are missing uniformly at random. In practice, however, that is not usually the case. This project will implement a method where the matrix completion problem can be solved under more realistic assumptions. This will impact all areas of science and technology where matrix completion algorithms have applications, such as recommender systems, collaborative filtering, computer vision, and genetics, to name a few. The second class of problems concerns the development of an approach for measuring conditional dependence. Measuring conditional dependence is important in many applications of statistics, such as in the analysis of graphical and causal models, which are widely used in the social sciences. The third class of problems is about developing a new approach for selecting the right variables for performing regression analysis when presented with a large number of variables. This part of the project will impact all areas of science and technology where regression problems with many predictors are commonplace, such as biology, medicine, and genomics.The project on matrix completion aims to solve the low rank matrix completion problem when the pattern of missing entries is deterministic. The PI has recently published an asymptotic solution of the problem. The project will yield a non-asymptotic version of the theory, and an algorithm for matrix completion when the probability of an entry to be missing is a function of the entry itself. The project on a new measure of conditional dependence will analyze the asymptotic properties of a coefficient proposed recently by the PI and one of his students. The results of the analysis may help in devising new tests for conditional independence. The project on feature selection will analyze the properties of a non-parametric feature selection algorithm proposed recently by the PI and one of his students. The results of the analysis may guide better implementation of the algorithm, as well as yield new and better selection algorithms.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
本课题主要研究数理统计中的三类问题。第一类问题是关于矩阵完备化的。假设我们有一个缺少条目的数字数组,比如一个产品用户评分的数据库。矩阵完备化是预测缺失值的问题。在过去的十年里,人们对这个问题做了很多工作,但绝大多数都是在假设矩阵元素均匀随机缺失的情况下进行的。但实际上,情况通常并非如此。这个项目将实现一种方法,可以在更现实的假设下解决矩阵完成问题。这将影响矩阵补全算法应用的所有科学和技术领域,例如推荐系统,协同过滤,计算机视觉和遗传学等。第二类问题涉及到发展一种测量条件依赖的方法。测量条件依赖性在统计学的许多应用中很重要,例如在社会科学中广泛使用的图形和因果模型的分析中。第三类问题是关于开发一种新的方法来选择正确的变量进行回归分析时,提出了大量的变量。该项目的这一部分将影响所有科学和技术领域,其中许多预测因子的回归问题是司空见惯的,如生物学,医学和基因组学。矩阵补全项目旨在解决低秩矩阵补全问题时,丢失的条目的模式是确定的。PI最近发表了这个问题的渐近解。该项目将产生一个非渐近版本的理论,和一个算法的矩阵完成时,一个条目的概率是一个函数的条目本身。这个关于条件依赖的新度量的项目将分析PI和他的一个学生最近提出的一个系数的渐近性质。分析的结果可能有助于设计新的条件独立性测试。关于特征选择的项目将分析PI和他的一名学生最近提出的非参数特征选择算法的属性。分析的结果可以指导算法的更好的实现,以及产生新的和更好的选择algorithm.This奖项反映了NSF的法定使命,并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

期刊论文数量(6)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Matrix Completion With Data-Dependent Missingness Probabilities
具有数据相关缺失概率的矩阵补全
  • DOI:
    10.1109/tit.2022.3170244
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    2.5
  • 作者:
    Bhattacharya, Sohom;Chatterjee, Sourav
  • 通讯作者:
    Chatterjee, Sourav
Weak convergence of directed polymers to deterministic KPZ at high temperature
高温下定向聚合物与确定性 KPZ 的弱收敛
  • DOI:
    10.1214/22-aihp1287
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Chatterjee, Sourav
  • 通讯作者:
    Chatterjee, Sourav
Superconcentration in surface growth
表面生长超浓缩
  • DOI:
    10.1002/rsa.21108
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    1
  • 作者:
    Chatterjee, Sourav
  • 通讯作者:
    Chatterjee, Sourav
Local KPZ Behavior Under Arbitrary Scaling Limits
任意缩放限制下的局部 KPZ 行为
Existence of stationary ballistic deposition on the infinite lattice
无限晶格上存在静止弹道沉积
  • DOI:
    10.1002/rsa.21116
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    1
  • 作者:
    Chatterjee, Sourav
  • 通讯作者:
    Chatterjee, Sourav
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Sourav Chatterjee其他文献

Spectral gap of nonreversible Markov chains
不可逆马尔可夫链的谱隙
  • DOI:
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sourav Chatterjee
  • 通讯作者:
    Sourav Chatterjee
MetQuan - A Comprehensive Toolkit for Variational Quantum Sensing and Metrology
MetQuan - 用于变分量子传感和计量的综合工具包
Retraction Note: ICB3E induces iNOS expression by ROS-dependent JNK and ERK activation for apoptosis of leukemic cells
  • DOI:
    10.1007/s10495-024-02007-7
  • 发表时间:
    2024-07-23
  • 期刊:
  • 影响因子:
    8.100
  • 作者:
    Nabendu Biswas;Sanjit K. Mahato;Avik Acharya Chowdhury;Jaydeep Chaudhuri;Anirban Manna;Jayaraman Vinayagam;Sourav Chatterjee;Parasuraman Jaisankar;Utpal Chaudhuri;Santu Bandyopadhyay
  • 通讯作者:
    Santu Bandyopadhyay
Liouville Theory: An Introduction to Rigorous Approaches
刘维尔理论:严格方法简介
  • DOI:
  • 发表时间:
    2024
  • 期刊:
  • 影响因子:
    0
  • 作者:
    Sourav Chatterjee;Edward Witten
  • 通讯作者:
    Edward Witten
RETRACTED ARTICLE: ICB3E induces iNOS expression by ROS-dependent JNK and ERK activation for apoptosis of leukemic cells
  • DOI:
    10.1007/s10495-011-0695-9
  • 发表时间:
    2012-01-18
  • 期刊:
  • 影响因子:
    8.100
  • 作者:
    Nabendu Biswas;Sanjit K. Mahato;Avik Acharya Chowdhury;Jaydeep Chaudhuri;Anirban Manna;Jayaraman Vinayagam;Sourav Chatterjee;Parasuraman Jaisankar;Utpal Chaudhuri;Santu Bandyopadhyay
  • 通讯作者:
    Santu Bandyopadhyay

Sourav Chatterjee的其他文献

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{{ truncateString('Sourav Chatterjee', 18)}}的其他基金

Mathematical Foundations for Yang-Mills Theory, Randomly Growing Surfaces, and Related Systems
杨米尔斯理论、随机生长曲面和相关系统的数学基础
  • 批准号:
    2153654
  • 财政年份:
    2022
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
Two-Dimensional KPZ Evolution, Fluctuation Lower Bounds, and Ultrametricity
二维 KPZ 演化、波动下界和超计量性
  • 批准号:
    1855484
  • 财政年份:
    2019
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Lattice Gauge Theories, Importance Sampling, and Quantum Unique Ergodicity
格规理论、重要性采样和量子唯一遍历性
  • 批准号:
    1608249
  • 财政年份:
    2016
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Concentration of measure, large deviations, normal approximation and applications
测量集中、大偏差、正态近似及应用
  • 批准号:
    1441513
  • 财政年份:
    2013
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Concentration of measure, large deviations, normal approximation and applications
测量集中、大偏差、正态近似及应用
  • 批准号:
    1309618
  • 财政年份:
    2013
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Random Structures and Limit Objects
随机结构和限制对象
  • 批准号:
    1237838
  • 财政年份:
    2012
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant
Disordered systems, dense graphs, normal approximation and applications
无序系统、稠密图、正态逼近及应用
  • 批准号:
    1005312
  • 财政年份:
    2010
  • 资助金额:
    $ 30万
  • 项目类别:
    Continuing Grant
Normal Approximation, Fair Allocations, Interacting Brownian Particles, and Applications
正态近似、公平分配、相互作用的布朗粒子和应用
  • 批准号:
    0707054
  • 财政年份:
    2007
  • 资助金额:
    $ 30万
  • 项目类别:
    Standard Grant

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